fast and curious

Thai's Teaser #49: Gold in Them Thar Hills

I just came back from a school camping trip to gold rush territory here in California and I can tell you the gold rush spirit is alive and well in kids today. How long would you think they can spend elbow deep in dirty water panning for little flakes of gold? We may never know the answer because we had to drag them away.

But with the California Gold Rush of 1849 on the brain, here's your teaser for your Memorial Day weekend.

James came to California to find his fortune in the Gold Rush. His first stop after arriving was the supply store where he bought the tools he needed to strike it rich. He knew he needed a weights and a balance to weigh all the gold he was surely going to find. He wanted to measure any whole number of ounces from 1 ounce to at least 12 ounces, and he already brought with him a 1-oz and a 9-oz weight. What size weight or weights should he buy?

Ready for the answer?

This isn't too hard; I think the easiest way is to take a few guesses and see if you make measure every weight between 1 and 12 ounces. Play around a bit and you'll find the answer is that James needs to buy just a 3-oz weight and that's it!

I'm leaving how that works for all whole ounce measurements for you to work out on your own, but if you get stuck, here's one answer: you can measure 7 ounces with the 9-oz and 1-oz weights on one side of the balance, and the 3-oz weight on the other side.